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Zbl 1092.03028
Şahin, Mehmet
Generalized fuzzy sets. (English)
[J] Proc. Jangjeon Math. Soc. 8, No. 2, 153-158 (2005). ISSN 1598-7264

Summary: Our aim is to generalize Lemma 2 and Lemma 3 of {\it N. Nakajima}'s article ``Generalized fyzzy sets'' [Fuzzy Sets Syst. 32, 307--314 (1989; Zbl 0676.06017)]. In this article, a construction of fuzzy sets without depending on a membership function, algebraic properties of a family of fuzzy sets, a ring of generalized fuzzy sets $\text{GF}(X)$ of $X$, a complete Heyting algebra (cHa) which contains the power set $P(X)$ of $X$, an extension lattice $\overline {B(L)}$ where $B=P(X)$, and the set of ${\bold L}$-fuzzy sets where ${\bold L}=\{Lx\mid x\in X\}$ were proposed and shown that they are equivalent depending on Lemma 2 and Lemma 3. In his article Lemma 2, Lemma 3 were not shown in their generalized version. In our article we show that these lemmas can be generalized.

MSC 2000:: *03E72 Fuzzy sets (logic)
06D20 Heyting algebras

Citations: Zbl 0676.06017

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